However, Relic grade equips cannot be fused, they're found in the Advanced Dungeons.
When fusing Legendary or Unique grade equips, keep in mind that they cannot exceed Lvl 120. Any Unique/Legendary equip that's 130+ have been obtained through Capsules.

*Tip, Do alot of dungeons to obtain high grade equips you can use to fuse and make better equips that you need. Advanced Dungeons and Daily Boss Dungeons have a high drop rate for high grade equips.

Minimum level requirements are listed under the description of each dungeon in the dungeon tab. I would check to see what the req for the first dungeon (Stumpy) is, but the server is down at the moment.

Not sure if it is just bad luck, but when I fuse it seems that the item is more likely to remain the same grade if I fuse it with either an equal grade or one grade below; every time I've fused either Rare or Unique with a Normal grade, the item with a higher grade downgrades. Somehow downgrading is more infrequent if I fuse with only one grade down (so Rare with Magic, Unique with Rare). Has anyone else noticed this, or am I just unlucky?

Yep! I was definitely wrong. Fusing with level 1 equips is the way to go, and to get higher level equips (130+) from fusing, don't use higher than Rare grade. Sometimes I get mad/frustrated/impatient and start fusing Rares+ with Magic grade items because my limited Inventory slots make things difficult, but in general, I wouldn't recommend fusing two higher grade (anything above normal) equips together. As the OP stated. Haha.